Microbial insecticide model and homoclinic bifurcation of impulsive control system  

作　　者：Tieying Wang 

机构地区：[1]School of Information and Cyber Security People’s Public Security University of China Beijing 100038,P.R.China

出　　处：《International Journal of Biomathematics》2021年第6期173-187,共15页生物数学学报（英文版）

摘　　要：A new microbial insecticide mathematical model with density dependent for pest is proposed in this paper.First,the system without impulsive state feedback control is considered.The existence and stability of equilibria are investigated and the properties of equilibria under different conditions are verified by using numerical simulation.Since the system without pulse has two positive equilibria under some additional assumptions,the system is not globally asymptotically stable.Based on the stability analysis of equilibria,limit cycle,outer boundary line and Sotomayor's theorem,the existence of saddle-node bifurcation and global dynamics of the system are obtained.Second,we consider homoclinic bifurcation of the system with impulsive state feedback control.The existence of order-1 homoclinic orbit of the system is studied.When the impulsive function is slightly disturbed,the homoclinic orbit breaks and bifurcates order-1 periodic solution.The existence and stability of order-1 periodic solution are obtained by means of theory of semi-continuous dynamic system.

关 键 词：Mathematical model of microbial insecticide state feedback control system homoclinic orbit homoclinic bifurcation. 

分 类 号：O17[理学—数学]